Question: Calculate the product below and give your answer in scientific notation. $ {\left(2\times 10^{6} \right) \times \left(0.00009 \right) =\ ?} $
Answer: First, let's change the second factor into scientific notation. $(2.0\times 10^{6}) \times (0.00009) = (2.0\times 10^{6}) \times (9.0\times 10^{-5}) $ Start by collecting the significands and exponents. $ ({2.0} \times {10^{6}}) \times ({9.0} \times {10^{-5}}) = ({2.0} \times {9.0}) \times ({10^{6}} \times {10^{-5}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {18.0} \times {10^{6 \,+\, -5}}$ $= {18.0} \times {10^{1}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${18.0}$ is the same as ${1.80 \times 10}$ or ${1.80 \times 10^{1}}$. $ = {1.80 \times 10^{1}} \times {10^{1}} $ $ = 1.80 \times 10^{{1} + {1}} $ $= 1.80\times 10^{2}$